Order of operations
What comes first? Enter your calculation and see every step — so you can find exactly where your own working went a different way.
The explanation is shown. Quick: enter the calculation and get the answer. Advanced: also see what you get if you forget the rule — and the examples worked out.
Your numbers
Use + − · : ^ and brackets. You can also type * for multiply and / for divide.
Answer
Result
15
How to work it out
- 3 + 4 · (2 − 5) ^ 2 : 3
- =3 + 4 · (−3) ^ 2 : 3
- =3 + 4 · 9 : 3
- =3 + 36 : 3
- =3 + 12
- =15
The formula
- Brackets first — the innermost before the outer ones.
- Powers and roots.
- Multiplication and division, from left to right.
- Addition and subtraction, from left to right.
In depth: more numbers and “what if”
If you forget the rule and calculate from left to right, you get 147 instead of 15. That is the typical mistake. The calculation took 5 steps.
The examples: correct and from the left
| Calculation | With the rule | From the left |
|---|---|---|
| 3 + 4 · (2 − 5)^2 : 3 | 15 | 147 |
| 12 − 3 · 2 + 8 : 4 | 8 | 6.5 |
| (5 + 3) · (10 − 4) : 2 | 24 | 24 |
| 2^3 + 4 · 5 − 6 | 22 | 54 |
More: Numbers and percentages
- PercentPercentage of, how many per cent, percentage change, discount and VAT.
- FractionsAdd, subtract, multiply and divide fractions — and simplify the answer.
- Powers and rootsPowers, square roots, nth roots and numbers as powers of 10.
- Primes and divisorsIs it a prime? Prime factors, divisors, GCD and LCM.
- Rounding and estimatingRound to decimals, tens or significant figures — and make an estimate.
- Number systems and Roman numeralsBinary, hexadecimal and Roman numerals — converted both ways with working.